A view of Nat as a quotient of some number and a finite remainder.
Converts Nat to the fractional view with a non-zero divisor.
Proof that double inversion of Fin n gives the original.
Proof that an element n of Fin m , when converted to Nat is smaller than the bound m.
Proof that application of finToNat the last element of Fin S n gives n.
Proof that an element n of Fin m , when converted to Nat is smaller than the bound m.
Enumerate elements of Fin n backwards.
Proof that an inverse of the last element of Fin (S n) in FZ.
Proof that an inverse of a weakened element of Fin n is a successive of an inverse of an original element.
Either tightens the bound on a Fin or proves that it's the last.
Proof that it's not possible to strengthen the last element of Fin n.
Proof that it's possible to strengthen an inverse of a succesive element of Fin n.
Proof that it's possible to strengthen a weakened element of Fin m.